Applied Mathematics & Information Sciences

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South Africa


In Appadu(2012d), we have used the technique of Minimized Integrated Exponential Error for Low Dispersion and Low Dissipation, (MIEELDLD) to construct high order methods with low dispersion and low dissipation properties which approximate the 1D linear advection equation. Modifications to the spatial discretisation schemes constructed by Lockard et al. (1995), Zingg et al. (1996) and Bogey and Bailly (2002) have been obtained and also a modification to the temporal scheme developed by Tam et al. (1993) has been devised. These novel methods obtained using MIEELDLD are more effective in terms of shock-capturing properties as they require less number of points per wavelength than the existing optimized methods for a given accuracy. In this paper, we perform some numerical experiments dealing with wave propagation with these novel as well as existing, combined spatial and temporal discretisation schemes and compare the variation of two errors namely the Total Mean Square Error and error rate with the CFL. The spectral analysis of two optimized methods made up of spatial discretisation scheme coupled with temporal discretisation scheme is also studied.

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